As in [1]} (or [2]}) pointed out, there exist some suitably small \( \tilde{\delta } > 0 \)  such that for
\(\left(v_{+}, u_{+}, \theta _{+}\right) \in R_{1} C R_{3}\left(v_{-}, u_{-}, \theta _{-}\right), \quad \left| \theta _+ - \theta _- \right| \le \tilde{\delta },\) 
